Which of the following quantity has dimensional formula as `(ML^(-1)T^(-2))`?

Options

A. Temperature
B. Kinetic energy
C. Pressure
D. Angular Speed

Answer

To determine which quantity has the dimensional formula \(ML^{-1}T^{-2}\), we will analyze the dimensional formulas of various physical quantities.

### Step 1: Identify the quantities to analyze
We need to check the dimensional formulas of the following quantities:
1. Temperature
2. Kinetic Energy
3. Pressure
4. Angular Speed

### Step 2: Analyze each quantity

1. **Temperature**:
- The dimensional formula of temperature is denoted as \(T\).
- **Dimensional Formula**: \(T\)

2. **Kinetic Energy**:
- Kinetic energy is given by the formula \(KE = \frac{1}{2}mv^2\).
- Here, \(m\) has the dimension of mass, which is \(M\), and \(v\) (velocity) has the dimension \(L T^{-1}\).
- Therefore, \(v^2\) has the dimension \(L^2 T^{-2}\).
- Thus, the dimensional formula for kinetic energy is:
\[ KE = M \cdot (L^2 T^{-2}) = ML^2 T^{-2} \]
- **Dimensional Formula**: \(ML^2 T^{-2}\)

3. **Pressure**:
- Pressure is defined as force per unit area.
- The dimensional formula for force is \(F = ma = MLT^{-2}\).
- Area has the dimension \(L^2\).
- Therefore, the dimensional formula for pressure is:
\[ P = \frac{F}{\text{Area}} = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2} \]
- **Dimensional Formula**: \(ML^{-1}T^{-2}\)

4. **Angular Speed**:
- Angular speed is defined as the angle (in radians) per unit time.
- The angle is dimensionless, and time has the dimension \(T\).
- Therefore, the dimensional formula for angular speed is:
\[ \text{Angular Speed} = \frac{\text{Angle}}{T} = \frac{1}{T} \]
- **Dimensional Formula**: \(T^{-1}\)

### Step 3: Conclusion
From the analysis, we find that the only quantity with the dimensional formula \(ML^{-1}T^{-2}\) is **Pressure**.

### Final Answer
The quantity that has the dimensional formula \(ML^{-1}T^{-2}\) is **Pressure**.

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